Solid State Sciences 17 (2013) 40e45
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Single crystal growth and structural characterization of four complex uranium oxides: CaUO4, b-Ca3UO6, K4CaU3O12, and K4SrU3O12 Cory M. Read, Daniel E. Bugaris, Hans-Conrad zur Loye* Department of Chemistry and Biochemistry, University of South Carolina, 631 Sumter Street, Columbia, SC 29208, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 October 2012 Received in revised form 9 December 2012 Accepted 17 December 2012 Available online 27 December 2012
Single crystals of complex uranium oxides, CaUO4, b-Ca3UO6, K4CaU3O12 and K4SrU3O12 were grown from carbonate melts. The crystal structures of the four uranates were determined by single crystal X-ray diffraction. CaUO4 crystallizes in the hexagonal space group R-3m, with lattice parameters a ¼ 6.2570(7) A and a ¼ 36.04(2) . The U6þ atom in CaUO4 is 8-coordinate and exhibits hexagonal bipyramidal geometry with six long and two short UeO bonds, typical of a uranyl species. b-Ca3UO6 forms in the monoclinic space group P21/n, with lattice parameters a ¼ 5.728(1) A, b ¼ 5.956(1) A, c ¼ 8.298(2) A, and b ¼ 90.55(3) , and adopts a distorted double perovskite structure. K4CaU3O12 and K4SrU3O12 crystallize in the cubic space group Im-3m with lattice parameters a ¼ 8.483(1) A and a ¼ 8.582(1) A, respectively. In all three perovskite-type oxides, the U(VI) cation is located in an octahedral coordination environment and exhibits typical uranyl geometry with four long and two short UeO bonds. Ó 2012 Elsevier Masson SAS. All rights reserved.
Keywords: Oxides Crystal growth Single crystals Uranium Complex uranium oxides Carbonate flux
1. Introduction Molten hydroxides and carbonates have been used with excellent success for the crystal growth of complex oxides containing elements from all groups of the periodic table [1,2]. Perhaps not surprisingly, only a relatively small number of oxide crystals containing actinide elements are found in the literature, although recently several reports have appeared detailing the crystal growth of uranium containing oxides out of both hydroxides and carbonate melts, including K2UO4, Na4UO5, Sr3UO6, Ba2MUO6 (M ¼ Cu, Ni, Zn), Ba2Na0.83U1.17O6, K4BaU3O12, and Na3Ca1.5UO6 [3e5]. Uranium containing complex oxides have been of interest for decades and, hence, a large number of reports detailing the synthesis and structures of polycrystalline powders of binary and ternary uranates can be found in the literature. In uranates, uranium typically assumes the þ6 oxidation state in the form of the uranyl cation, UO2 2þ , which can occur in structures containing chains or layers of uranium polyhedral networks. If one considers the variety of uranium containing structures that have been reported, uranium is most commonly found in an octahedral coordination environment. Since U6þ is a fairly large cation, with
ionic radius ¼ 0.73 A (CN ¼ 6) [6], not every structure type is able to accommodate the large UO6 octahedra. Nevertheless, a variety of structure types containing U6þ are known, including alkali metal uranates [7], alkaline earth uranates [8,9], and mixed metal uranates [10]. Recently there has been renewed interest in uranium oxides due to the unsettled issue of long term nuclear waste storage and also because of the ongoing development of new fuel rod technologies. Thus, it is of fundamental interest to investigate the structureeproperty relationships of uranium oxides and especially to pursue the preparation of new complex uranium oxides. Herein we report the crystal growth and structure determination of four uranium containing oxides, CaUO4, b-Ca3UO6, K4CaU3O12, and K4SrU3O12 that were all prepared as single crystals in molten carbonates fluxes. The syntheses of polycrystalline powders of CaUO4 [9,11], b-Ca3UO6 [12,13], K8Ca2U6O24, and K8Sr2U6O24 [14] have been reported previously, yet this is the first time single crystals have been grown and characterized, further displaying the versatility of the potassium carbonate melt as a medium for crystal growth of complex uranium containing oxides. 2. Experimental details
* Corresponding author. Tel.: þ1 803 777 6916; fax: þ1 803 777 8508. E-mail addresses:
[email protected],
[email protected] (H.-C. zur Loye). 1293-2558/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.solidstatesciences.2012.12.013
Caution: UO2 and U3O8 contain depleted uranium, but standard precautions for handling radioactive and highly toxic substances should be followed.
C.M. Read et al. / Solid State Sciences 17 (2013) 40e45
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Single crystals of K4SrU3O12 were grown from a molten potassium carbonate flux. 0.33 mmol of U3O8 (MV Laboratories, 99.9%), 3 mmol of SrCO3 (Alfa, 99.99%), and 10 g of K2CO3 (JT Baker, A.C.S. grade) were loaded into an alumina crucible and covered with an alumina disc. The charge was placed into a tube furnace and heated in air at a rate of 600 C/h to 1050 C. The furnace was held at this temperature for 24 h, after which time it was cooled at a rate of 5 C/h to 800 C, and subsequently cooled to room temperature by switching off the furnace. Amber, plate crystals of CaUO4, yellow, prismatic crystals of bCa3UO6, and orange, block crystals of K4CaU3O12 and K4SrU3O12 were isolated from the solidified fluxes by dissolving the fluxes with water, assisted by ultrasonication, and collected by vacuum filtration. The observed colors are typical for U6þ compounds. An optical image of K4SrU3O12 crystals is shown in Fig. 1. 2.2. Single crystal X-ray diffraction Single crystal X-ray diffraction data were collected with the use of A) at 298 K graphite monochromatized MoKa radiation (l ¼ 0.71073 on a Bruker SMART APEX CCD diffractometer. The crystal-to-detector distance was 5.048 cm for CaUO4 and b-Ca3UO6, and 5.081 cm for K4CaU3O12 and K4SrU3O12. Crystal decay was monitored by recollecting the 50 initial frames at the end of the data collection. Data were collected by a scan of 0.3 in u in groups of 606 frames at 4 settings of 0 , 90 , 180 , and 270 . The exposure time was 10 s/frame for b-Ca3UO6, 15 s/frame for CaUO4, and 20 s/frame for K4CaU3O12 and K4SrU3O12. The collection of intensity data was carried out with the program SMART [15]. Cell refinement and data reduction were carried out with the use of the program SAINTþ [15]. A numerical absorption correction was performed with the use of the program SADABS [15]. The program SADABS was also employed to make incident beam and decay corrections. The structure was solved with the direct methods program SHELXS and refined with the full-matrix least-squares program SHELXL [16]. The final refinement included anisotropic displacement parameters. A secondary extinction correction was included for the refinement of K4SrU3O12. The previously published atomic coordinates for CaUO4 [11], as determined by powder X-ray diffraction, were used as a starting
Fig. 1. An optical image showing the orange block crystals of K4SrU3O12. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2.1. Crystal growth Single crystals of CaUO4, b-Ca3UO6, and K4CaU3O12, were grown from a molten potassium carbonate flux. For CaUO4 and b-Ca3UO6, 1 mmol of UO2 (Strem, 99.8%), 3 mmol of CaCO3 (Alfa, 99.95%), and 10 g of K2CO3 (Alfa, 99.0%) were loaded into alumina crucibles covered with alumina discs. The charges were placed into a tube furnace that was then purged with N2 gas. The furnace was heated at a rate of 600 C/h to 900 C. The furnace was maintained at this temperature for 48 h with a constant flow of N2. The charge was finally cooled to room temperature by switching off the furnace. When the identical reaction is performed in air, single crystals of K4CaU3O12 can be recovered instead as the major phase. Table 1 Crystal structure and refinement data for CaUO4, b-Ca3UO6, K4CaU3O12, and K4SrU3O12.a Compound
CaUO4
b-Ca3UO6
K4CaU3O12
K4SrU3O12
Formula weight Color and habit Space group Z a ( A) b ( A) c ( A) a ( ) b ( ) V ( A3) rc (g cm3) m (mm1) F(000) Crystal size (mm) qmax ( ) Index ranges
342.11 Amber plate R-3m 1 6.2570(7) 6.2570(7) 6.2570(7) 36.04(2) 36.04(2) 75.84(2) 7.491 55.010 144 0.12 0.07 0.05 28.24 8 h 8; 8 k 8; 8 l 8 1009 92 1.211 R1 ¼ 0.0112, wR2 ¼ 0.0264 1.908/0.800
454.27 Yellow prism P21/n 2 5.728(1) 5.956(1) 8.298(2) 90.00 90.55(3) 283.1(1) 5.329 31.344 400 0.22 0.04 0.03 28.23 7 h 7; 7 k 7; 11 l 11 3699 702 1.050 R1 ¼ 0.0169, wR2 ¼ 0.0445 1.825/2.258
1102.57 Orange block Im-3m 2 8.483(1) 8.483(1) 8.483(1) 90.00 90.00 610.5(1) 5.998 41.534 936 0.08 0.07 0.07 28.29 11 h 11; 11 k 11; 11 l 11 4195 98 1.210 R1 ¼ 0.0106, wR2 ¼ 0.0267 1.978/0.451
1150.11 Orange block Im-3m 2 8.582(1) 8.582(1) 8.582(1) 90.00 90.00 632.0(1) 6.044 43.892 972 0.03 0.03 0.02 27.94 11 h 11; 11 k 11; 11 l 11 4258 100 1.345 R1 ¼ 0.0094, wR2 ¼ 0.0316 0.750/0.763
Reflections collected Independent reflections Goodness-of-fit on F2 R indices (all data) Largest difference peak/hole (e A3) a
For all structures, T ¼ 298(2) K and l ¼ 0.71073 A.
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model for the refinement. This refinement proceeded without difficulty and rapidly converged to satisfactory R values. The largest A3, located 0.94 A difference map extrema are þ1.91 and 0.80 e/ and 0.85 A from U, respectively. The previously published atomic coordinates for b-Ca3UO6 [13], as determined by powder neutron diffraction, were used as a starting model for the refinement. The refinement rapidly converged to R values of R1 ¼ 0.0220 and wR2 ¼ 0.0580. However, the thermal parameter of Ca(2) remained non-positive definite. Allowing the site occupancy of Ca(2) to refine freely, the value of the site occupancy increased above 1.0, indicating the presence of more electron density on the site. Therefore, U was added to the site, and again the occupancies were allowed to refine freely. This resulted in approximately 95% Ca and 5% U on the site, and significantly improved the R values to R1 ¼ 0.0160 and wR2 ¼ 0.0431. However, with a formula of Ca2(Ca0.95U0.05)UO6, the implication is that there is slightly reduced U in the compound (wU5.81þ), which is unlikely given that the compound was synthesized in an oxidizing environment, as evidenced by the fully oxidized CaUO4 that was isolated from the same reaction. Thus, a model with anti-site mixing on the B and B0 sites (constrained to be the same value) between Ca and U was chosen, and by trial-and-error, a value of 4% anti-site mixing was found to be most satisfactory. The refinement converged to R values of R1 ¼ 0.0169 and wR2 ¼ 0.0445, where the A3, located largest difference map extrema are þ1.82 and 2.26 e/ 0.83 A and 0.78 A from U(3)/Ca(3), respectively. The previously published atomic coordinates for “K8Ca2U6O24” [14], as determined by powder X-ray diffraction, were used as a starting model for the refinements of K4CaU3O12 and K4SrU3O12. The refinements proceeded without difficulty and rapidly converged to satisfactory R values. In both cases, the six-coordinate 2a site was fully occupied by the alkaline-earth element, and the 8c site was occupied entirely by K. The structure report for K4BaU3O12 [5] indicated that the 2a site was occupied by K instead of the alkaline earth element, and the 8c site was occupied by a 75/25
Table 2 Atomic coordinates and equivalent isotropic displacement parameters for CaUO4, bCa3UO6, K4CaU3O12, and K4SrU3O12. Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. x
y
z
Ueq
Occupancy
0.5 0 0.1116(3) 0.3621(4)
0.5 0 0.1116(3) 0.3621(4)
0.5 0 0.1116(3) 0.3621(4)
0.0062(4) 0.0050(2) 0.008(1) 0.008(1)
1 1 1 1
0.5139(1) 0.5 0.5 0 0 0.1761(4) 0.2966(4) 0.3735(4)
0.5523(2) 0 0 0.5 0.5 0.2117(4) 0.6776(4) 0.9321(4)
0.24304(9) 0 0 0 0 0.9219(3) 0.9448(3) 0.2666(3)
0.0130(1) 0.0057(2) 0.0057(2) 0.0049(1) 0.0049(1) 0.0166(5) 0.0168(5) 0.0128(4)
1 0.96 0.04 0.04 0.96 1 1 1
K4CaU3O12 K 0.25 Ca 0 U 0 O(1) 0.2743(6) O(2) 0.25
0.25 0 0.5 0 0
0.25 0 0 0 0.5
0.0144(6) 0.0076(6) 0.0049(2) 0.015(1) 0.017(1)
K4SrU3O12 K 0.25 Sr 0 U 0 O(1) 0.2793(7) O(2) 0.25
0.25 0 0.5 0 0
0.25 0 0 0 0.5
0.0151(7) 0.0092(4) 0.0060(2) 0.023(1) 0.024(2)
CaUO4 Ca U O(1) O(2)
b-Ca3UO6 Ca(1) Ca(2) U(2) Ca(3) U(3) O(1) O(2) O(3)
Table 3 Selected interatomic distances ( A) and angles ( ) for CaUO4. UeO(1) 2 UeO(2) 6
1.957(6) 2.291(2)
CaeO(2) 2 CaeO(1) 6
2.418(6) 2.434(3)
O(2)eUeO(2) O(1)eUeO(2) O(1)eUeO(1) O(2)eUeO(2)
64.7(1) 77.3(2) 180.0(1) 180.0(1)
O(1)eCaeO(2) O(1)eCaeO(1) O(1)eCaeO(1) O(2)eCaeO(2)
66.7(1) 74.7(1) 180.0 180.00(4)
mixture of K and Ba, rather than by K. Trial refinements in the current examples with Ca and Sr showed no evidence of this site exchange. For K4CaU3O12, the largest difference map extrema A3, located 0.00 A and 1.00 A from Ca, are þ1.98 and 0.45 e/ respectively. For K4SrU3O12, the largest difference map extrema A3, located 0.16 A and 0.25 A from K and Sr, are þ0.75 and 0.76 e/ respectively. As noted previously for K4BaU3O12, the disk-shaped thermal displacement ellipsoids of the O atoms (more pronounced for the Sr compound) indicate that there may be some disorder to a slight perovskite tilt system. However, this could not be resolved from the single-crystal X-ray diffraction data. Relevant crystallographic information from the single crystal structure refinement for CaUO4, b-Ca3UO6, K4CaU3O12, and K4SrU3O12 is compiled in Table 1 and atomic positions for the title compounds are given in Table 2. Selected interatomic distances are tabulated in Tables 3e5. 2.3. Energy-dispersive spectroscopy (EDS) Elemental analysis was performed on the flux-grown crystals using an FEI Quanta 200 scanning electron microscope (SEM) with EDS capabilities. The crystals were mounted on carbon tape and analyzed using a 30 kV accelerating voltage and an accumulation time of 20 s. As a qualitative measure, the EDS confirmed the presence of each reported element in the title compounds. An SEM image of a CaUO4 plate crystal can be seen in Fig. 2. 3. Results and discussion CaUO4 crystallizes in the hexagonal space group R-3m. The structure consists of alternating UO4 and Ca layers (Fig. 3). Within the structure the UO8 polyhedra share edges with neighboring UO8 polyhedra to form a two-dimensional sheet (Fig. 4), and share faces in the third dimension with CaO8 polyhedra. The same is true for the CaO8 polyhedral sheets. The UO8 hexagonal bipyramids (Fig. 5) exhibit a coordination motif consistent with the uranyl species [17], with six long equatorial UeO bonds and two short axial UeO bonds at 2.291(2) and 1.957(6) A, respectively. The rhombohedral SrUO4 polymorph is isostructural showing the same UO8 coordination Table 4 Selected interatomic distances ( A) and angles ( ) for b-Ca3UO6.
1 1 1 1 1
Ca(1)eO(3) Ca(1)eO(1) Ca(1)eO(2) Ca(1)eO(3) Ca(1)eO(1) Ca(1)eO(2) Ca(1)eO(2)
2.332(2) 2.348(2) 2.348(2) 2.410(3) 2.655(2) 2.821(3) 2.859(3)
Ca(2)/U(2)eO(2) 2 Ca(2)/U(2)eO(1) 2 Ca(2)/U(2)eO(3) 2
2.290(2) 2.330(2) 2.369(2)
U(3)/Ca(3)eO(2) 2 U(3)/Ca(3)eO(1) 2 U(3)/Ca(3)eO(3) 2
2.057(2) 2.097(2) 2.101(2)
1 1 1 1 1
O(1)eCa(2)/U(2)eO(1) O(1)eCa(2)/U(2)eO(2) O(1)eCa(2)/U(2)eO(3) O(2)eCa(2)/U(2)eO(2) O(2)eCa(2)/U(2)eO(3) O(3)eCa(2)/U(2)eO(3)
180.0(2) 89.76(7) 84.13(8) 180.0(1) 83.35(8) 180.0(2)
O(1)eU(3)/Ca(3)eO(1) O(1)eU(3)/Ca(3)eO(2) O(1)eU(3)/Ca(3)eO(3) O(2)eU(3)/Ca(3)eO(2) O(2)eU(3)/Ca(3)eO(3) O(3)eU(3)/Ca(3)eO(3)
180.0 87.23(8) 87.97(9) 180.0(1) 88.50(9) 180.0(1)
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Table 5 Selected interatomic distances ( A) and angles ( ) for K4CaU3O12 and K4SrU3O12. M ¼ Ca
M ¼ Sr
KeO(2) 6 KeO(1) 6 MeO(1) 6 UeO(1) 2 UeO(2) 4
2.9993(4) 3.0063(5) 2.327(5) 1.915(5) 2.1208(3)
3.0340(4) 3.0444(6) 2.397(6) 1.894(6) 2.1454(3)
O(1)eKeO(1) O(1)eKeO(1) O(1)eKeO(2) O(1)eKeO(2) O(2)eKeO(2) O(2)eKeO(2) O(1)eCaeO(1) O(1)eCaeO(1) O(1)eUeO(1) O(1)eUeO(2) O(2)eUeO(2)
66.4(2) 180.0 56.82(8) 90.0 60.0 180.0 90.0 180.0 180.0 90.0 180.0
67.7(2) 180.0 56.17(9) 90.0 60.0 180.0 90.0 180.0 180.0 90.0 180.0
[11]. Several other compounds display the UO8 hexagonal bipyramids, and are compiled in an extensive review by Burns [18]. The three remaining structures presented here belong to the cubic perovskite family of oxides. The simple cubic perovskite structure is of the form ABO3, where corner-sharing BO6 octahedra link together to form a 12-coordinate, cubic coordination environment that is occupied by the A cation. This structure is quite flexible, accommodating many different cations, and variations can occur if there are multiple cations on the B site. An example is the double perovskite of the form, A2BB0 O6. It is important to note that, in cases where the A cation is too small or the B cation is too large, the structure can undergo distortions into tetragonal and monoclinic crystal systems to allow for favorable AeO and BeO binding interactions. These distortions are exhibited by tilting of the BO6 octahedra. The Goldschmidt tolerance factor, t, relates the radii of the ions in the perovskite and is used to help predict this tilting. For the double perovskite, t ¼ (rA þ rO)/[O2 (0.5rB þ 0.5rB0 þ rO)], [19,20]. If t ¼ 1, the structure is cubic. If t < 1, the symmetry is lowered to tetragonal or even monoclinic for smaller values of t. b-Ca3UO6 crystallizes in the P21/n space group, and is the high temperature polymorph. The low temperature polymorph, a-Ca3UO6
Fig. 2. An SEM image of plate-like single crystal of CaUO4.
Fig. 3. The crystal structure of CaUO4, where UO8 polyhedra are shown in green and Ca2þ and O2e atoms are shown as blue and red spheres, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
crystallizes in the rhombohedral space group R-3 [21]. The title compound, b-Ca3UO6 is a member of the double perovskite family of oxides, A2BB0 O6, where U occupies the B0 site, and Ca occupies both the A and the B sites (Fig. 6). The structure consists of alternating, corner-shared CaO6 and UO6 octahedra. The corner-shared octahedra form a cubic coordination environment that is occupied by the remaining Ca atoms. Because the Ca atom is relatively small for the A site in this structure, the CaO6 and UO6 octahedra must tilt in order to allow for favorable bonding interactions, resulting in CaO8 polyhedra on this A site and monoclinic symmetry for the extended structure. The Goldschmidt tolerance factor is 0.79 for this structure, consistent with the observed monoclinic distortion. Uranium exhibits the typical uranyl coordination environment, where it has two short Ue O axial bonds of 2.057(2) A, and four UeO equatorial bonds with lengths greater than 2.09 A. Anti-site mixing on the B and B0 sites was observed in the single-crystal X-ray diffraction structure refinement process. K4CaU3O12 and K4SrU3O12 are isostructural and crystallize in the Im-3m space group. Mudher et al. [14] previously published the structures of “K8M2U6O24” (M ¼ Ca, Sr, Ba) as determined by
Fig. 4. A representation of the uranyl sheets in CaUO4 from the top, where UO8 polyhedra are shown in green and the oxygen atoms are shown as red spheres. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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C.M. Read et al. / Solid State Sciences 17 (2013) 40e45
Fig. 5. A representation of the UO8, uranyl environment in CaUO4, where U6þ and O2e are shown as green and red spheres, respectively. O1 labels represent the axial ligands, while O2 labels represent the equatorial ligands. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Rietveld refinement of powder X-ray diffraction data. It was recently shown via single crystal diffraction studies that the K8Ba2U6O24 structure reported by Mudher was not entirely accurate [5]. These two compositions represent another variation of the cubic perovskite structure, where one alkaline-earth atom and three uranium atoms occupy the B site in an ordered fashion (Fig. 7). The majority of the other known cubic perovskites of this type exhibit mixing on the A site, as in CaCu3Mn4O12 [22] and NaMn7O4 [23]. CaCu3Ga2M2O12 (M ¼ Sb, Ta) exhibits ordering of both the A and the B site cations, such that (Ca,Cu) and (Ga,M) occupy the A and B sites, respectively [24]. Ba4LiSb3O12 exhibits B site ordering, as seen in the title compounds [25]. The structures of the two title compounds, K4MU3O12 (M ¼ Ca, Sr) consist of ordered, corner-shared BO6 octahedra containing M and U that arrange to form a cubic site that is occupied by 12coordinate K. The KO12 and CaO6 or SrO6 polyhedra are regular,
Fig. 7. The crystal structure of K4MU3O12 (M ¼ Ca, Sr), where UO6 and MO6 octahedra are shown in green and blue, respectively. The A site Kþ atoms are shown as violet spheres. The oxygen atoms were removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
while the UO6 octahedra exhibit the typical uranyl coordination with the two shorter axial UeO bonds and four longer equatorial UeO bonds. The two axial oxygen atoms are shared with neighboring CaO6 or SrO6 octahedra, while the four equatorial oxygen atoms are shared with neighboring UO6 octahedra. 4. Conclusions Single crystals of CaUO4, b-Ca3UO6, K4CaU3O12 and K4SrU3O12 were grown for the first time. All of the crystals reported here were isolated from potassium carbonate melts, exhibiting further variation in the U6þ containing structures and compositions that can be synthesized in the carbonate flux. Acknowledgments Research supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008664. Appendix A. Supporting information Further details of the crystal structure investigation can be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: þ49 7247808666; e-mail: crystdata@fiz-karlsruhe.de) on quoting the depository numbers CSD-425120, CSD-425121, CSD-425122, and CSD-425123. References
Fig. 6. The crystal structure of Ca3UO6, where UO6 and CaO6 octahedra are shown in green and blue, respectively. The A site Ca2þ atoms are shown as blue spheres. The oxygen atoms were removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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